Definition:Ordered Semigroup Automorphism

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Definition

Let $\struct {S, \circ, \preceq}$ be an ordered semigroup.

An ordered semigroup automorphism from $\struct {S, \circ, \preceq}$ to itself is a mapping $\phi: S \to S$ that is both:

$(1): \quad$ A semigroup automorphism, that is, a semigroup isomorphism from the semigroup $\struct {S, \circ}$ to itself
$(2): \quad$ An order isomorphism from the ordered set $\struct {S, \preceq}$ to itself.


Also see


Linguistic Note

The word automorphism derives from the Greek morphe (μορφή) meaning form or structure, with the prefix iso- meaning equal.

Thus automorphism means self structure.


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